1 True.
2 False. In Elizabethan slang ‘‘nunnery’’ meant ‘‘brothel’’.
3 False. It took place on Breed’s Hill, and the Revolutionaries lost.
4 True. It comes from the Latin minutus (small) – not because they record
minute-by-minute proceedings.
5 False. What he wrote was “Foolish consistency is the hobgoblin of little minds.” That’s different.
6 True. Ice cream is loaded with calories, and that makes you hotter.
7 True. The claim that Epicurus was a hedonist is a slander. He taught an untroubled, contented mind as the key to happiness.
8 True and false. They are correctly so pronounced. But the explanation is that the settlers did not have enough lower case ‘n’s in their font, so they had to be omitted in print.
9 True. The Greeks called it Persia, the Iranians chose to use its true name.
10 False. It may of course be small and a portrait, but the name comes from miniare – to colour with red lead. Originally used for illustrating manuscripts.
11 True. For example, Inuits are stubby to cope with the cold, and Maasai are tall to cope with the heat.
12 False. Istanbul is a contraction of a Greek phrase: eis ten pólin (to the city).
13 True. Thomas Sanchez SJ, 16th century, approved this view.
14 False. Tulips come from central Asia, and were first introduced into Europe by an ambassador to the Turkish court.
15 True. It can only detect stress-related signs which may be associated with lying.
16 False. There is no time in purgatory, nor is purgatory a place.
17 False. It is not an artichoke and it does not originate from Jerusalem. It is a sunflower, for which the Italian word is girasole (sun-turner).
18 True. Or, if not true, he never mentioned it – nor did anyone else until years later.
19 False. It was introduced, as medicine, by the Spanish physician Francisco Fernandez in 1558. It became popular in the Elizabethan court some 30 years later.
20 False. No mention is made of an apple.
21 True. The first successful aeroplane flew in 1896. It was steam-powered and had no passenger.
22 False. Although popularly ascribed to her, the incident was first recorded 15 years before she was born.
23 True. Commonly, the intestines of sheep are used.
24 True.
25 False. The skin only takes in negligible oxygen.
26 False. All cattle, including bulls, are red/green colour-blind. Both colours are monochrome to them.
27 False. It ended up on the mountains of Ararat. No single mountain is mentioned.
28 True. The phrase is not found in Conan Doyle’s stories and novels.
29 True. A Muslim sect called Quakers were seen to “swell, shiver and shake” in Southwark in 1647 (not the Society of Friends).
30 Happy Christmas!

Sources. A wide range of sources have been used from Aquinas to Pascal to the OED. Of particular value have been The Dictionary of Misinformation Tom Burnham and The Natural History of Nonsense Bergen Evans.

I have seen the “official” answer to #2 in a book on misconceptions, but it does not explain why Hamlet would utter “Why wouldst thou be a breeder of sinners?” prior to that line. Did the Elizabethan slang-mongers have the opinion that no children are ever conceived in brothels? Or that abortion methods would be universally applied in brothels?

Regarding #16, I see no theological reason for assuming that there is “no time in purgatory,” especially since all our conscious experience, including suffering, is inextricably connected with time. I suspect that this part of the answer is due to confusion about a misconception concerning the old-fashioned “partial indulgences” that had a time (like seven years for praying “My Lord and my God” at the Elevation) associated with them. This did not refer to a shortening of the time spent in purgatory, but to a ridiculously generous substitute for that much time spent in the kind of penance one did in the early days of the Church.

Regarding #22, I have read that “cake” is a mistranslation for a kind of roll, and that it was a naive question along the lines of “Why is that a problem? Can’t they get rolls instead?”

Concerning #28, it depends on how one defines “Sherlock Holmes”. The Holmes character does utter that line in an old film, not scripted by Arthur Conan Doyle.